As disclosed in Patent Literature 1, there is a flow rate control apparatus including: a flow rate sensor, an upstream side valve provided on the upstream side of the flow rate sensor, and a downstream side valve provided on the downstream side of the flow rate sensor. In such a flow rate control apparatus, the upstream side valve is fed back with a measured pressure measured by a pressure sensor, and the opening level thereof is controlled. Also, the downstream side valve is fed back with a measured flow rate measured by the flow rate sensor, and the opening level thereof is controlled.
Meanwhile, the position of the flow rate sensor and the position of the downstream side valve are displaced from each other in a flow direction, and therefore a time delay occurs in the measured flow rate measured by the flow rate sensor with respect to a flow rate actually through the downstream side valve.
Such a time delay causes a delay in flow rate control, and therefore an attempt is made to perform flow rate control in which a control point and a measurement point are matched by estimating the actual flow rate through the downstream side valve as a valve flow rate and feeding back the estimated valve flow rate.
Specifically, the valve flow rate is estimated by measuring the pressure between the flow rate sensor and the downstream side valve and from the flow rate measured by the flow rate sensor, subtracting a value obtained by multiplying the time differential value of the pressure by a constant determined from the gas state equation.
However, since the time differential value of the pressure is used in order to estimate the valve flow rate, noise superimposed on the measured pressure is amplified by the differentiation, and large noise may continue to occur in the estimated valve flow rate as well. If flow rate control is performed based on such a valve flow rate, for example, even in a steady state, the valve flow rate may be unstable within a tolerance.